28663 ÷ 6 = 4777 R1
Alright, let's work through the division of 28663 by 6 step by step.

Step 1:
6 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (8) of the dividend behind the 2 and repeat the process: 28 / 6

Step 2:
6 goes into 28 4 times with a remainder of 4.
Write down 4 as next digit of of the result. 
Result so far: 4
Subtract 24 from 28 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 6

Step 3:
6 goes into 46 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 47
Subtract 42 from 46 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 6

Step 4:
6 goes into 46 7 times with a remainder of 4.
Write down 7 as next digit of of the result. 
Result so far: 477
Subtract 42 from 46 to get 4.
Bring next digit (3) of the dividend behind the 4 and repeat the process: 43 / 6

Step 5:
6 goes into 43 7 times with a remainder of 1.
Write down 7 as next digit of of the result. 
Result so far: 4777
Subtract 42 from 43 to get 1.

The final result is 4777 with a remainder of 1.